Further developments in <Emphasis Type="Italic">J</Emphasis> evaluation procedure for growing cracks based on LLD and CMOD data

Laboratory testing of fracture specimens to measure resistance curves (J − Δa) have focused primarily on the unloading compliance method using a single specimen. Current estimation procedures (which form the basis of ASTM E1820 standard) employ load line displacement (LLD) records to measure fracture toughness resistance data incorporating a crack growth correction for J. An alternative method which potentially simplifies the test procedure involves the use of crack mouth opening displacement (CMOD) to determine both crack growth and J. However, while the J-correction for crack growth effects adopted by ASTM standard holds true for resistance curves measured using load line displacement (LLD) data, it becomes unsuitable for J-resistance measurements based upon the specimen response defined in terms of load-crack mouth opening displacement (CMOD). Consequently, direct application of the evaluation procedure for J derived from LLD records in laboratory measurements of resistance curves using CMOD data becomes questionable. This study provides further developments of the evaluation procedure for J in cracked bodies that experience ductile crack growth based upon the eta-method and CMOD data. The introduction of a constant relationship between the plastic components of LLD (Δ _p ) and CMOD (V _p ) drives the development of a convenient crack growth correction for J with increased loading when using laboratory measurements of P-CMOD data. The methodology broadens the applicability of current standards adopting the unloading compliance technique in laboratory measurements of fracture toughness resistance data (J resistance curves). The developed J evaluation formulation for growing cracks based on CMOD data provides a viable and simpler test technique to measure crack growth resistance data for ductile materials.     

Limitations of elastic definitions in Al-Si-Mg cast alloys with enhanced plasticity: linear elastic fracture mechanics versus elastic-plastic fracture mechanics

Linear elastic fracture mechanics describes the fracture behavior of materials and components that respond elastically under loading. This approach is valuable and accurate for the continuum analysis of crack growth in brittle and high strength materials; however it introduces increasing inaccuracies for low-strength/high-ductility alloys (particularly low-carbon steels and light metal alloys). In the case of ductile alloys, different degrees of plastic deformation precede and accompany crack initiation and propagation, and a non-linear ductile fracture mechanics approach better characterizes the fatigue and fracture behavior under elastic-plastic conditions.To delineate plasticity effects in upper Region II and Region III of crack growth an analysis comparing linear elastic stress intensity factor ranges (ΔK_el) with crack tip plasticity adjusted linear elastic stress intensity factor ranges (ΔK_pl) is presented. To compute plasticity corrected stress intensity factor ranges (ΔK_pl), a new relationship for plastic zone size determination was developed taking into account effects of plane-strain and plane-stress conditions (“combo plastic zone”). In addition, for the upper part of the fatigue crack growth curve, elastic-plastic (cyclic J based) stress intensity factor ranges (ΔK_J) were computed from load-displacement records and compared to plasticity corrected stress intensity factor ranges (ΔK_pl). A new cyclic J analysis was designed to compute elastic-plastic stress intensity factor ranges (ΔK_J) by determining cumulative plastic damage from load-displacement records captured in load-control (K-control) fatigue crack growth tests. The cyclic J analysis provides the true fatigue crack growth behavior of the material. A methodology to evaluate the lower and upper bound fracture toughness of the material (J_IC and J_max) directly from fatigue crack growth test data (ΔK_FT(JIC) and ΔK_FT(Jmax)) was developed and validated using static fracture toughness test results. The value of ΔK_FT(JIC) (and implicitly J_IC) is determined by comparing the plasticity corrected elastic fatigue crack growth curve with the elastic-plastic fatigue crack growth curve. A most relevant finding is that plasticity adjusted linear elastic stress intensity factor ranges (ΔK_pl) are in remarkably good agreement with cyclic J analysis results (ΔK_J), and provide accurate plasticity corrections up to a ΔK corresponding to J_IC (i.e. ΔK_FT(JIC)). Towards the end of the fatigue crack growth test (above ΔK_FT(JIC)) when plasticity is accompanied by significant tearing, the cyclic J analysis provides a more accurate way to capture the true behavior of the material and determine ΔK_FT(Jmax). A procedure to decouple and partition plasticity and tearing effects on crack growth rates is given.Three cast Al-Si-Mg alloys with different levels of ductility, provided by different Si contents and heat treatments (T61 and T4) are evaluated, and the effects of crack tip plasticity on fatigue crack growth are assessed. Fatigue crack growth tests were conducted at a constant stress ratio, R = 0.1, using compact tension specimens.     

The effect of T-stress on plane strain dynamic crack growth in elastic–plastic materials

In this paper, the effects of T‐stress on steady, dynamic crack growth in an elastic–plastic material are examined using a modified boundary layer formulation. The analyses are carried out under mode I, plane strain conditions by employing a special finite element procedure based on moving crack tip coordinates. The material is assumed to obey the J₂ flow theory of plasticity with isotropic power law hardening. The results show that the crack opening profile as well as the opening stress at a finite distance from the tip are strongly affected by the magnitude and sign of the T‐stress at any given crack speed. Further, it is found that the fracture toughness predicted by the analyses enhances significantly with negative T‐stress for both ductile and cleavage mode of crack growth.     

On the fitting and extrapolation of J-resistance data derived through the linear normalization technique

In this paper, an assessment is made regarding the effects of J–R curve fitting and extrapolation methods in two J‐integral criteria – namely crack initiation, J_i, and tearing instability, J₅₀– which were obtained through the linear normalization technique. Power‐law, logarithmic and linear fits were concurrently applied to J–Δa data derived from sub‐sized compact tensile specimens machined from a nuclear grade steel and tested at 300 °C. Research results show that the logarithmic J–R fit is the most conservative approach within a broad range of elastic–plastic fracture resistance, compared to the conventional power‐law fit. On the other hand, the linear fitting method provided the most non‐conservative J‐predictions. The values of J_i and J₅₀ have been successfully correlated with the net energy absorbed during Charpy impact testing of the materials.     

Fatigue life prediction and failure analysis of a gas turbine disc using the finite-element method

A numerical prediction of the life of a gas turbine model disc by means of the finite‐element technique is presented and the solution is compared with an experimental rim‐spinning test. The finite‐element method was used to obtain the K solution for a disc with two types of cracks, both at the notch root of the blade insert and located in the corner and in the centre. A crack aspect ratio of (a/c) = 1 was assumed. The fracture mechanics parameters J‐integral and K were used in the assessment, which were computed with linear elastic and elastic–plastic material behaviour. Using a crack propagation program with appropriate fatigue‐creep crack growth‐rate data, previously obtained in specimens for the nickel‐based superalloy IN718 at 600 °C, fatigue life predictions were made. The predicted life results were checked against experimental data obtained in real model discs. The numerical method, based on experimental fatigue data obtained in small laboratory specimens, shows great potential for development, and may be able to reduce the enormous costs involved in the testing of model and full‐size components.     

Plastic collapse load prediction and failure assessment diagram analysis of cracked circular hollow section T‐joint and Y‐joint

This paper concerns the validation of standard safety assessment procedure given in BS 7910 for cracked circular hollow section T‐joint and Y‐joint, using the finite element (FE) results. A robust and efficient FE mesh generator is developed to produce the 3D models of the cracked joints and to calculate the elastic J‐integral (J_e) and elastic–plastic J‐integral (J_ep) values of the crack respectively. In order to verify its accuracy and convergence, the plastic collapse loads (P_c) obtained from experimental tests and FE predictions are compared; they agree very well with each other. It is also found from experimental tests that the plastic collapse loads (P_c) predicted using the BS 7910 reduction factor (F_AR) are safe and conservative. Subsequently, the failure assessment diagrams (FADs) of five cracked T‐joints and three cracked Y‐joints are constructed using the FE results, following the J‐integral method, which is classified as Level 3C in BS 7910. Thereafter, a comparison between the constructed FAD curves and the standard Level 2A curve is carried out, and it is observed that the safety assessment results using the standard Level 2A curve might be unsafe because some parts of the constructed FAD curves fall inside of the standard one. A penalty factor of 1.15 working on both the elastic–plastic J‐integral and plastic collapse load (P_c) is proposed to move all the constructed FAD curves just outside of the standard Level 2A curve.     

Prediction of the energy dissipation rate in ductile crack propagation

In this paper, energy dissipation rate D vs. Δa curves in ductile fracture are predicted using a ‘conversion’ between loads, load‐point displacements and crack lengths predicted by NLEFM and those found in real ELPL propagation. The NLEFM/ELPL link was recently discovered for the DCB testpiece, and we believe it applies to other cracked geometries. The predictions for D agree with experimental results. The model permits a crack tip toughness R(Δa) which rises from J_c and saturates out when (if) steady state propagation is reached after a transient stage in which all tunnelling, crack tip necking and shear lip formation is established. J_R is always greater than the crack tip R(Δa) and continues to rise even after R(Δa) levels off. The analysis is capable of predicting the usual D vs. Δa curves in the literature which have high initial values and fall monotonically to a plateau at large Δa. It also predicts that D curves for CCT testpieces should be higher than those for SENB/CT, as found in practice. The possibility that D curves at some intermediate Δa may dip to a minimum below the levelled‐off value at large Δa is predicted and confirmed by experiment. Recently reported D curves that have smaller initial D than the D‐values after extensive propagation can also be predicted. The testpiece geometry and crack tip R(Δa) conditions required to produce these different‐shaped D vs. Δa curves are established and confirmed by comparison with experiment. The energy dissipation rate D vs. Δa is not a transferable property as it depends on geometry. The material characteristic R(Δa) may be the ‘transferable property’ for scaling problems in ELPL fracture. How it can be deduced from D vs. Δa curves (and by implication, J_R vs. Δa curves) is established.     

Characterization of the nonlinear fracture resistance parameters for an aviation GTE turbine disc

The effects of crack growth rate model formulation, based on the elastic‐plastic and undamaged/damaged creep crack tip fields on the behaviour of low‐cycle fatigue and creep fracture resistance parameter behaviour, are represented by numerical calculations. The crack growth rate models include the fracture process zone size and damage parameters. An aviation gas turbine engine (GTE) rotating turbine disc is the focus of this innovative application of basic analytical and numerical solutions. For the GTE turbine disc, the constraint parameters, local fracture process zone sizes, and nonlinear plastic (K_p) and creep (K_cr) stress intensity factors are calculated by finite element analysis to characterize the fracture resistance along the semielliptical crack front as a function of the flaw aspect ratio, operation temperature, and disc rotation speed. Predictions of the creep‐fatigue crack growth rate and residual lifetime are given for different combinations of operation loading conditions and damage of the GTE turbine disc.     

Three‐dimensional mixed‐mode (I and II) crack‐front fields in ductile thin plates — effects of T‐stress

It has been well‐established that the non‐singular T‐stress provides a first‐order estimate of geometry and loading mode (e.g. tension versus bending) effects on elastic–plastic crack‐front field under mode I loading conditions. The objective of this paper is to exam the T‐stress effect on three‐dimensional (3D) crack‐front fields under mixed‐mode (modes I and II) loading. To this end, detailed 3D small strain, elastic–plastic simulations are carried out using a 3D boundary layer (small‐scale yielding) formulation. Characteristics of near crack‐front fields are investigated for a wide range of T‐stresses (T/σ₀ = ?0.8, ?0.4, 0.0, 0.4, 0.8). The plastic zones and thickness and angular and radial variations of the stresses are studied, corresponding to two values of the remote elastic mixity parameters M_e = 0.3 and 0.7, under both low and high levels of applied loads. It is found that different T‐stresses have a significant effect on the plastic zones size and shapes, regardless of the mode mixity and load level. The thickness, angular and radial distributions of stresses are also affected markedly by T‐stress. It is important to include these effects when investigating the mixed‐mode ductile fracture failure process in thin‐walled structural components.     

On improved crack tip plastic zone estimates based on T‐stress and on complete stress fields

Cracked ductile structures yield locally to form a plastic zone (pz) around their crack tips, which size and shape controls their structural behaviour. Classical pz estimates are based solely on stress intensity factors (SIF), but their precision is limited to very low σ_n/S_Y nominal stress to yield strength ratios. T‐stresses are frequently used to correct SIF‐based pz estimates, but both SIF and SIF plus T‐stress pz estimates are based on truncated linear elastic (LE) stress fields that do not satisfy boundary conditions. Using Griffith's plate complete LE stress field to avoid such truncated pz estimates, the influence of its Williams’ series terms on pz estimation is evaluated, showing that T‐stress improvements are limited to medium σ_n/S_Y values. Then, corrections are proposed to introduce equilibrium requirements into LE pz estimates. Finally, these improved estimates are compared with pz calculated numerically by an elastic–plastic finite element analysis.     

General time‐dependent C(t) and J(t) estimation equations for elastic‐plastic‐creep fracture mechanics analysis

This paper presents equations for estimating the crack tip characterizing parameters C(t) and J(t), for general elastic‐plastic‐creep conditions where the power‐law creep and plasticity stress exponents differ, by modifying the plasticity correction term in published equations. The plasticity correction term in the newly proposed equations is given in terms of the initial elastic‐plastic and steady‐state creep stress fields. The predicted C(t) and J(t) results are validated by comparison with systematic elastic‐plastic‐creep FE results. Good agreement with the FE results is found.     

Unified characterisation of in‐plane and out‐of‐plane constraint based on crack‐tip equivalent plastic strain

Constraint can be divided into two conditions of in‐plane and out‐of‐plane, and each of them has its own parameter to characterize. However, in most cases, there exists a compound change of both in‐plane and out‐of‐plane constraint in structures, a unified measure that can reflect both of them is needed. In this paper, the finite element method (FEM) was used to calculate the equivalent plastic strain (ɛ_p) distribution ahead of crack tips for specimens with different in‐plane and out‐of‐plane constraints, and the FEM simulations based on Gurson–Tvergaard–Needleman (GTN) damage model and a small number of tests were used to obtain fracture toughness for the specimens with different constraints. Unified measure and characterisation parameter of in‐plane and out‐of‐plane constraints based on crack‐tip equivalent plastic strain has been investigated. The results show that the area A_PEEQ surrounded by the ɛ_p isoline ahead of crack tips can characterize both in‐plane and out‐of‐plane constraints. Based on the area A_PEEQ, a unified constraint characterisation parameter A_p was defined. It was found that there exists a sole linear relation between the normalised fracture toughness J_IC/J_ref and regardless of the in‐plane constraint, out‐of‐plane constraint and the selection of the ɛ_p isolines. The unified J_IC/J_ref−reference line can be used to determine constraint‐dependent fracture toughness of materials. The FEM simulations with the GTN damage model (local approach) can be used in obtaining the unified J_IC/J_ref−reference line for materials with ductile fracture.     

Effect of Constraint on the Fracture Behaviour of a Simulated Heat‐Affected Zone of an X‐70 Steel Used in Pipelines

Abstract: The typical heat‐affected zone developed in an X‐70 steel, usually used in pipeline manufacture, has been simulated via thermal treatment. A non‐equilibrium microstructure consisting of bainite, with ferrite and some martensite, has been produced and mechanically characterised, resulting in much greater hardness and strength and a lower ductility and toughness than the corresponding base metal. This also has a lower ductility. Different single‐edge notched bending specimens with different crack lengths (a/W between 0.1 and 0.5) were experimentally tested to assess the fracture behaviour of this product under different degrees of constraint. The J–a resistance curves at room temperature were determined, and the obtained results were explained by the effect of constraint on ductile crack growth.     

A review of the J and I integrals and their implications for crack growth resistance and toughness in ductile fracture

The application of the J and the I-integrals to ductile fracture are discussed. It is shown that, because of the finite size of the fracture process zone (FPZ), the initiation value of the J-integral is specimen dependent even if the plastic constraint conditions are constant. The paradox that the I-integral for steady state elasto-plastic crack growth is apparently zero is examined. It is shown that, if the FPZ at the crack tip is modelled, the I-integral is equal to the work performed in its fracture. Thus it is essential to model the fracture process zone in ductile fracture. The I-integral is then used to demonstrate that the breakdown in applicability of the J-integral to crack growth in ductile fracture is as much due to the inclusion in the J-integral of progressively more work performed in the plastic zone as it is to non-proportional deformation during unloading behind the crack tip. Thus J _R -curves combine the essential work of fracture performed in the FPZ with the plastic work performed outside of the FPZ. These two work terms scale differently and produce size and geometry dependence. It is suggested that the future direction of modelling in ductile fracture should be to include the FPZ. Strides have already been made in this direction.     

An analytical expression for the J2‐integral of an interfacial crack in orthotropic bimaterials

This paper presents a new analytical expression relating the J₂‐integral and stress intensity factors (SIF) in an in‐plane traction‐free crack between two orthotropic elastic solids using the complex function method. The singular oscillatory near tip field of a bimaterial interfacial crack is usually characterized by a pair of SIFs. In linear elastic interfacial fracture mechanics, the majority of numerical and experimental methods rely on the analytical equations relating J_k‐integrals and SIFs. Although an analytical equation relating J₁‐integral or strain energy release rate and SIFs is available, a similar relation for J₂‐integral in debonded anisotropic solids is non‐existent. Using this new analytical expression, in conjunction with the values of J_k, the SIFs can be computed without the need for an auxiliary relation. An example with known analytical solutions for SIFs is presented to show the variation of the J₂‐integral near the crack tip of a bimaterial orthotropic plate. Different bimaterial combinations are considered, and the effect of material mismatch on J_k is demonstrated.     

Transferability of the two‐parameter fracture criterion for 2219 aluminium alloy cracked configurations

Two‐dimensional elastic–plastic finite‐element fracture simulations with the critical crack‐tip‐opening‐angle fracture criterion were used to evaluate the two‐parameter fracture criterion (TPFC). Three different crack configurations under tension and bending loads made of thin‐sheet 2219‐T87 aluminium alloy were analysed. A very wide range of widths (w = 76 to 2440 mm) and initial crack‐length‐to‐width ratios (c_i/w = 0.05 to 0.95) were considered. A relation from the original TPFC was shown to fit the simulated fracture behaviour fairly well for the three different specimen types for net‐section stresses less than the yield stress (σ_y) of the material. Comparisons were also made on measured and simulated fracture tests on middle‐crack‐tension specimens. A relation between the elastic stress‐intensity factor, K_Ie, and net‐section stress, S_n, at failure was found to be linear for S_n < σ_y. The results demonstrated the transferability of the TPFC for different crack configurations for S_n < σ_y, but further study is needed for S_n > σ_y.     

Corrosion fatigue behaviour of a 15Cr‐6Ni precipitation‐hardening stainless steel in different tempers

Systematic fatigue experiments, including both high‐cycle axial fatigue (S–N curves) and fatigue crack growth (FCG, da/dN–ΔK curves), were performed on a precipitation‐hardening martensitic stainless steel in laboratory air and 3.5 wt% NaCl solution. Specimens were prepared in three tempers, i.e. solution‐annealed (SA), peak‐aged (H900) and overaged (H1150) conditions, to characterize the effects of ageing treatment on the corrosion fatigue (CF) resistance. S–N results indicated that fatigue resistance in all three tempers was dramatically reduced by the aqueous sodium chloride environment. In addition, the smooth‐surface specimens in H900 temper exhibited longer CF lives than the H1150 ones, while those in SA condition stood in between. However, for precracked specimens, the H1150 temper provided superior corrosive FCG resistance than the other two tempers. Comparison of the S–N and FCG curves indicated that early growth of crack‐like defects and short cracks played the major role in determining the CF life for smooth surface. The differences in the CF strengths for the S–N specimens of the given three tempers were primarily due to their inherent differences in resistance to small crack growth, as they were in the air environment.     

Fatigue crack growth model for constant amplitude loading

A fatigue crack growth model under constant amplitude loading has been developed considering energy balance during growth of the crack. The plastic energy dissipated during growth of a crack within cyclic plastic zone and area below cyclic stress–strain curve was used in the energy balance. The near crack tip elastic–plastic stress and strain were calculated on the basis of Hutchinson, Rice and Rosengren (HRR) formulations. Fatigue crack growth rate in linear and near threshold region of da/dN versus ΔK curve can be determined on the basis of the proposed model in terms of low cycle fatigue (LCF) properties determined on smooth specimen. The predictions of the model have been compared with the experimental and theoretical results available in the literature using mechanical and fatigue properties. The model compares well in the threshold and intermediate region of the da/dN versus ΔK curve for wide range of material tested.     

Numerical simulations to support the normalization data reduction technique

The normalization data reduction (NDR) technique is an analytical methodology for characterizing the upper shelf fracture toughness of steels in the ductile regime, both in terms of critical toughness (J_Ic) and resistance to ductile crack extension (J-R curve). It represents an alternative to the more commonly used multi-specimen or single-specimen (unloading compliance and potential drop) techniques.Finite element analyses of a growing crack are executed to evaluate the performance of the technique. This approach has the advantage to remove large uncertainties entailing experimental results. Results demonstrate the precision of the method.     

R-curve behaviour of a structural steel

The ductile tearing behaviour-of BS4360 50D structural steel has been studied using two bending specimen geometries: square (W = B) cross section three point bend specimens with different initial fatigue crack length, ranging from a/W = 0.20 to about 0.75, and rectangular cross section (W = 2B) specimens with initial fatigue crack length a/W = 0.3.With the first set of specimens it was intended to investigate the possible dependence of the tearing behaviour on initial crack length. It was concluded that specimens with shorter values of initial crack length present higher resistance to ductile tearing. Two different methods of calculating the J-resistance curve, one based on the approximate equation J = 2A/(W?a)B and a more elaborate calculation procedure introduced by Garwood were used. The curves determined following the more accurate procedure were used to determine the value of the tearing modulus T, which is related to the occurrence of tearing instabilities in structures. It was found that T decreases slightly with increasing value of initial crack length.The tests using the wider specimen geometry were intended to examine the tearing behaviour over a larger amount of crack growth allowed by the wider geometry used. It was found that the resistance curves, using the COD concept, present a maximum after which the resistance begins to drop. This maximum value of the COD-resistance curve is higher than the conventional δ_max measured at max load. These tests were performed using the compliance technique of evaluating the crack length. Tests performed with 10% unloading presented slightly lower values of resistance than tests performed with complete unloading.It was found that the relationship J = mσ_flowδδ presents increasing values of m with crack growth. This is attributed to an increasing local yield stress, caused by the through thickness deformation.